MATH 3210 Class Notes 02-14-2025

notevector-spaces

Fundamental Theorem of Linear Maps

Finished proof, and detailed several corollaries.

Representing Linear Maps by a Matrix

We know that if $v_1,\dots ,v_n$ is a basis of $V$ and $T:V\to W$ is a linear map, then the values of $T{v}_1,\dots ,T{v}_n$ completely determines the value of $T$ on arbitrary elements of $V$.

Defined Matrix (Representation of a Linear Map)